For example, JP-A-2003-256341 discloses a cellular phone device having a Bluetooth (BT: registered trademark) communication function. The cellular phone device is carried into a vehicle equipped with an in-vehicle apparatus having a BT communication function. When the cellular phone device receives an incoming mail from a communication network in a state where the cellular phone device is connecting to the in-vehicle apparatus via a BT communication, the cellular phone device transmits mail information related to an received e-mail, such as an incoming date, an incoming time, a sender, a subject name, a text, and the like. In the structure of JP-A-2003-256341, connection between the cellular phone device and the in-vehicle apparatus via the BT communication channel suffices a condition that the cellular phone device transmits the mail information, which is related to an e-mail received by the cellular phone device from the communication network, to the in-vehicle apparatus. By the transmission of the mal information, the mail information is synchronized between the cellular phone device and the in-vehicle apparatus. That is, a memory content of the cellular phone device is equalized to a memory content of the in-vehicle apparatus. Consequently, a user can use the mail information, which is related to an e-mail received by the cellular phone device from the communication network during connection of the BT communication channel, on the in-vehicle apparatus. Specifically, the user can cause the in-vehicle apparatus to indicate a text or a list of subject names included in the mail information.
However, in the structure of JP-A-2003-256341, the mail information related to an e-mail, which is received by the cellular phone device from the communication network during disconnection of the BT communication channel, is not synchronized between the cellular phone device and the in-vehicle apparatus. Accordingly, a user cannot use the mail information related to an e-mail, which is received by the cellular phone device from the communication network during disconnection of the BT communication channel, on the in-vehicle apparatus. So as to solve such a problem, it is conceivable that the cellular phone device transmits all the mail information stored in the cellular phone device to the in-vehicle apparatus immediately after the cellular phone device connects with the in-vehicle apparatus via the BT communication channel. However, when the cellular phone device transmits all the mail information stored in the cellular phone device, the transmission of all the mail information takes a long time.